A recent and notable evolution in the development of medicines is the use of pharmaco-imaging to measure pharmacokinetic parameters. In a known manner, pharmacokinetics is the component of pharmacology which describes the disposition of medicines in the organism, and specifies in a qualitative and quantitative manner the processes of absorption, distribution, metabolization and elimination of an active principle.
The great advantage of pharmaco-imaging as compared with conventional techniques, which require the repeated extraction of biological samples, is its ability to measure the concentration of the active principle in the organs of the human patient or live animal. One thus avoids the need to sacrifice batches of animals, and one substantially decreases the dispersion of values—all the measurements of the kinetics being made in the same animal. Moreover, the kinetics can be analyzed in the deep organs in man.
On the other hand, pharmaco-imaging requires an implementation which may be technologically unwieldy: firstly marking, radioactive or other, of the active principle to be tracked; next, proof that the detection by imaging does indeed give a quantitative measure of the concentration of the active principle; finally, the tagging of the anatomical location of the signal related to the marked active principle.
In a general but not exclusive manner, a preferred technique of pharmaco-imaging is positon emission tomography (PET) which, on account of the principle of detection on which it is based, is among the imaging techniques best suited to quantitative measurements of molecular concentrations in human or animal organs.
In any event, the measurement of the concentration of a marked active principle (hereinafter called a tracer) at a point of the organism studied is only interpretable from the pharmacokinetic standpoint if it is possible to assign this point to a defined organ, either on an anatomical basis, or on a physiological basis: the heart, the liver, the kidney, a tumor, a region of the brain, etc. However, the image is solely representative of the location of the indicator (radioactive positon emitter in the case of PET) related to the active principle studied, and does not contain a priori any anatomical or physiological information, but solely pharmacokinetic information. It is therefore necessary to superimpose the successive images of location of the tracer on one or more images providing clues about the anatomy and/or physiology. This superposition or registration may be done in several ways:                In the most favorable and least frequent case, the distribution of the tracer discloses a recognizable anatomy. This is the case for tracers that concentrate in the whole of a notable anatomical system such as the skeleton, which do not require additional registration, all the information being in the image. Conversely, this is also the case for certain tracers which diffuse very well in all organs (for example fluorodeoxyglucose). In the latter case, the organs are delimited on the images by a contrast dependent on the level of retention of the tracer, this not necessarily being sufficient for their identification, for example in the case of two adjoining organs having the same tracer retention level. In a general manner, this case where registration is of little or no use relates only to “generalist” tracers (ions, metabolic precursors etc.) and not to the imaging of active principles.        In numerous other cases, the organs are tagged by “overlaying” of an anatomic image emanating from the examiner's knowledge about pharmaco-images. A biologist may often guess the location of anatomical organs, such as the liver or the heart, on the images whose contrast scale tracks the dynamics of the concentration of the tracer. The accuracy of location obtained then depends on the ability to identify the organ, hence on the distribution of the tracer which to a greater or lesser extent delimits the contours of an organ, and on the skill or experience of the examiner. It is understood that this method without anatomical image is inapplicable to the case of a tracer which is present at just one point.        Increasingly often, the examiner calls upon a second image which he superimposes on the pharmaco-image, via a second mode of imaging in which the contrast is not based on location of the tracer but on anatomy (for example tomodensitometry, or magnetic resonance imaging or MRI) which is applied to the same individual, preferably during the same imaging session. By superimposing the two images, the pharmaco-image is registered on an anatomical image which identifies the organs. This dual modality is being increasingly widely used for clinical imaging with the recent advent of the “PET-CT” system associating PET camera and X-ray tomodensitometer. However, the dual modality is not totally satisfactory for pharmaco-imaging for both fundamental and practical reasons:        From the fundamental standpoint, the anatomical image merely overlays static information on the pharmaco-kinetic information given by the pharmaco-image. The link, other than the subject, between the anatomical image and the pharmaco-image can therefore be established only if the pharmacokinetic location of the tracer exactly tracks the organ contours described by the anatomical image. Consequently, the additional information afforded by the anatomical image is limited to the resolution of the anatomical imaging method used, which is far from always being sufficient to identify the nature of all pharmaco-organs. For example, tomodensitometry affords little contrast in soft tissues and the brain, MRI distinguishes pulmonary masses poorly, etc.        From the practical standpoint:        Coupled cameras of “PET-CT” type are currently available only for man, hence with a large aperture and a lower resolution than PET cameras dedicated to small animals. These cameras are necessarily more expensive than PET cameras alone.        In the case of anatomical imaging by tomodensitometry, the irradiation dose required to obtain an image in a small rodent is far from being negligible. This poses problems of toxicity and/or of interpretation of results in the case of the imaging of tumors.        The registration quality obtained is contingent on the total immobility of the subject throughout the duration of the pharmacokinetics explored, this not being the case when transporting an animal from one camera to another.        
Additionally, the pharmacokinetic interpretation of PET images generally requires the delimitation of regions of interest (“ROI”) representative of the organs. Kimura and coll. [Kimura, 2002] and Zhou [Zhou, 2003] have shown that a suitable grouping of volume elements (voxels) improves the quality of the pharmacokinetic quantification. Specifically, the tracing of the regions of interest presupposes that each organ or part of an organ exhibits homogeneous behavior in respect of a given tracer, which may be characterized by physiological kinetics. Consequently, whatever the method of segmentation, the outlines of the organs traced must be visible in order to prevent the regions of interest from encompassing two organs or parts of organs with different functions (called pharmaco-organs hereinafter). The quality of the segmentation of the image into regions of interest that are consistent from the pharmacokinetic standpoint is therefore crucial. However, the regions of interest are in general traced manually, this being a lengthy and irksome job dependent on the operator and requiring a certain degree of expertise.
A certain number of works, whose aim was not limited to the pharmacokinetic analysis of images, have proposed methods of automatic segmentation making it possible to dispense with the operator for the segmentation of the regions of interest. PET images suffer from a low signal-to-noise ratio. Since they also suffer from low spatial resolution, the activity measured at a given volume element of the image is polluted by the activity contained in the neighboring volume elements. In particular, the measurement of the concentration of the tracer in the organs of small size may either be underestimated, or overestimated depending on whether the radioactive concentration in the surrounding structures is higher or lower. This so-called “partial volume” effect may in fact be modeled as a smoothing of the image [Frouin, 2002] and therefore renders the contours of the organs intrinsically fuzzy. As a consequence, the parts of the organs near the boundaries of the latter will not contain the kinetics of a single pharmaco-organ, but a linear combination of the kinetics of all the nearby pharmaco-organs. Thus, the kinetics of the pharmaco-organ most represented within a volume element is not necessarily that of the pharmaco-organ(s) actually contained in this volume element.
Furthermore, dynamic PET images represent in a known manner a large mass of data (some half a million kinetics), the processing of which is prohibitive in terms of calculation time and computer memory required [Guo, 2003]. In the images, the organism studied represents between 20% and 40% of the data. The remaining part, outside the organism, contains mainly noise.
It is known moreover that the kinetics within a volume element (this term designates the elementary volume unit of the image) is meaningful only on condition that the pharmaco-organ studied is perfectly immobile during the image sequence acquisition time. Any motion of the pharmaco-organ imaged breaks the link between the kinetics of a volume element and the kinetics of this pharmaco-organ. Physiological motions, which are extremely difficult to correct, are of two kinds.
Certain motions are periodic, with a period that is generally less than the duration of acquisition of an image of the sequence. Heart beats and respiration impose a displacement of the neighboring organs, generating a blurring effect which is not negligible, but almost constant from one acquisition to the next.
Other non periodic motions are unpredictable, such as the movement of the viscera during digestion and under the effect of respiration, or the filling of the bladder during the examination: the apparent volume of the bladder may increase tenfold between the start and the end of the examination. For tracers excreted in the urine, the concentration of the tracer and of the metabolites in the urine becomes very high. A voxel corresponding to a visceral or muscular region at the start of the examination may therefore contain a kinetic characteristic of the bladder at the end of the examination. As shown in FIG. 2 attached, the filling of the bladder generates a family of kinetics composed for the early acquisition times of the kinetics of a pharmaco-organ near to the bladder, and for the later times of the kinetics of the bladder. The hypothesis of a fixed number of kinetics contained in a PET image, to within noise and the partial volume effect, does not therefore apply in the case of an imaged organism subject to non periodic physiological motions.
Finally, it is known that the noise in PET images differs according to the methods of reconstructing images used.
Within an image arising from an analytical reconstruction by filtered retroprojection, the noise is often considered to be stationary Gaussian additive in the image, and uncorrelated with the signal. On the other hand, the noise of an image of the sequence depends on the duration of acquisition of this image. This dependency may be considered to be linear [Guo, 2003] with respect to the inverse of the duration of acquisition of the image.
In the images arising from iterative statistical methods, such as “OSEM” (“Ordered Subset Expectation Maximization”, method reconstructing the image by maximizing the likelihood of its projection according to various angles of incidence) or “AWOSEM” (“Attenuation Weighted Ordered Subset Expectation Maximization”, method operating in a similar manner to “OSEM” by taking into account the phenomenon of attenuation of the photons by the organism), it is no longer possible to assume stationary noise in space. The noise depends on the number of iterations used for the reconstruction, stationary phenomenon, but is also correlated with the signal. We can write: σ2=α2×S, where σ represents the local variance of the noise at a given instance, α a constant independent of position and time, but dependent on the method of reconstruction used and on the number of iterations chosen, and S the signal at the point considered. In this particular case, the signal-to-noise ratio is expressed as S/σ=α×S1/2. The separation of the noise and of the signal at any point of the image allows the calculation of α and makes it possible to finely characterize the noise. As in the case of reconstruction by an analytic method, the data should be corrected for the influence of the duration of acquisition of each image of the sequence.
Several methods of segmenting PET images into aggregates grouping together zones with homogeneous kinetics, without a prior anatomical knowledge, have recently been proposed in order to attempt to solve the aforementioned problems.
Ashburner [Ashburner, 1996] assumes that a PET image contains a known number of kinetics—one per aggregate—, and therefore describes any kinetic of a voxel of the image as the kinetic of an aggregate, multiplied by a scale factor, to which is added multinormal Gaussian noise—with a normal law for each image acquired—identical for each aggregate.
Wong and coll. [Wong, 2002] assume the kinetics to be homogeneous within one and the same aggregate, but dissimilar between different aggregates. They propose an aggregation approach by the k-means method, which maximizes the variance of the kinetics between the classes, while minimizing the variance of the kinetics within one and the same class. The kinetic of an aggregate is then estimated as the mean of the kinetics of the individuals of which it is composed.
Frouin F. and coll. [Frouin, 2001] also use the k-means method to produce a segmentation of the heart on perfusion images. However, the aggregation is not done on the kinetics themselves, but on factors extracted from the kinetics by factorial analysis, ensuring better robustness of the segmentation. However, the interpretation of the factors of a factorial analysis becomes difficult beyond 4 or 5 factors, thus excluding its direct use on a whole body. It will be noted that the method described by Frouin F. and coll does not segment an organism into pharmaco-organs, but a pharmaco-organ into zones of preeminence of factors such as the arterial, veinous and tissular kinetics.
Acton [Acton, 1999] uses the method of fuzzy c-means, much like k-means, but allowing better account to be taken of the intrinsically fuzzy nature of the data acquired in tomography by simple photons, while ensuring better robustness.
Kimura and coll. [Kimura, 2002] propose a method of aggregation over the projections of the kinetics onto the eigenvectors associated with the two largest eigenvalues of a principal component analysis performed on the whole set of kinetics of the organism, so as to extract compartmental modeling parameters.
Brankov and coll. [Brankov, 2003] propose a use of a similarity measure defined as the cosine of the angle formed between two vectors represented in the kinetics space, rather than a Euclidian norm or a total variance norm. This similarity measure exhibits strong sensitivity to noise in zones of low signal-to-noise ratio. Brankov and coll. present two algorithms of expectation-maximization type (“EM”), one fuzzy and the other binary, which determine aggregates within which the individuals—kinetics—exhibit strong similarity. The “EM” methodology makes it possible to iteratively estimate a hidden variable whose image is a particular realization conforming to a chosen model. Each iteration comprises a first expectation phase in which the expected likelihood of the complete data is calculated on the basis of the joint distribution of the observed and hidden data, and a second maximization phase in which the parameters of the model which maximizes this expected likelihood of the model are estimated. The process is repeated until the algorithm converges.
Brankov compares his method in particular with an application of mixtures of probabilistic principal component analyzers. This method, introduced by Tipping and Bishop [Tipping, 1999], models the signal within the zone to be segmented by a mixture of projections onto subspaces of the space of kinetics.
A major drawback of all these methods is that they are randomly initialized. At each run, the algorithm converges to one of its local minima. However, the solution sought corresponds a priori to the global minimum of this energy. Several runs of the program with different initializations each time are therefore necessary in order to approach the best solution.
Guo [Guo, 2003] proposes an aggregation by hierarchical ascending classification making it possible to obtain a number of aggregates that is defined a posteriori, but also to retain the aggregates of small size. For the calculation of the distance between kinetics, the value at the volume elements considered is weighted at each instant of the kinetic by the signal-to-noise ratio expected for the corresponding image. This ratio, for a given image of the sequence, is assumed to depend essentially on the duration of acquisition of this image. The hierarchical approach ensures the convergence of the algorithm to an optimal minimum, but at the price of a calculation time that does not allow the whole of the data volume to be examined. Moreover, any voxel merging obtained by this algorithm is definitive. Consequently, erroneous assignment of a voxel during the first few iterations, for example on account of noise, cannot be corrected during successive iterations.
Guo and coll. [Guo, 2003] propose a histogram-based presegmentation in order to obtain first groupings accelerating a hierarchical ascending classification. The latter operates by a succession of merges of individuals in an optimal order according to a chosen criterion. The two individuals—typically voxels of the image—that are closest in terms of a chosen distance are aggregated, then the aggregates or closest individuals are again aggregated, and so on and so forth until a stopping criterion is satisfied or else until there exists only one aggregate grouping together all the individuals. The histogram used by Guo and coll. can be described as a counting of the number of voxels having a given intensity. This histogram-based classification employs the values of the last image in the temporal sense of the series acquired after administration of the tracer. It is assumed that the first few merges have little impact on the final aggregates and the voxels corresponding to the same interval of the histogram of the last image of the sequence are grouped together. The variation in the spatial distribution is assumed to be minimal for this last image from among all those contained in the time interval considered, the tracer having had maximum time to disperse in the organs according to its affinity. However, in the case of the isotopes with short radioactive period used in PET, on account of the exponential decay of the radioactivity over time, this entails the drawback of increased noise because the last series also exhibits the lowest signal-to-noise ratio of all the images of the series.
Out of all these methods, only that of F. Frouin is validated on moving organs with small-period periodic type motions. However, on account of the principle thereof, it is applicable only to zones of the organism comprising very few pharmaco-organs. None of the other aforementioned methods has been validated in the case of a whole body problem area, and none are suitable for physiological motions specific to this problem area.
The patent document EP-A-1 365 356 presents a method of semi-automatic segmentation of images acquired by PET, which requires in particular the prior delineation of a region of interest and of model-voxels to be extracted from the images. It will be noted that the method presented in this latter document is limited to the field of oncology and that it does not enable the images to be segmented into as many regions of interest as pharmaco-organs, but only into two parts just one of which contains a tumor.